1. Field of the Invention
This invention relates to a method and an apparatus for determining the size of a single fine particle and the size distribution of a group of fine particles.
2. Description of the Prior Art
Recently, submicron particles are widely used in manufacturing advanced ceramics, super-conductive materials, magnetic materials, pigments etc. Accurate determination of the size or size distribution of these fine particles are desired more than ever.
For the size determination of particles larger than one micron, diffraction-based instruments is widely used. In these instruments, the scattered light from a group of particles illuminated by a parallel laser beam is collected by an optical lens placed forwardly and the angular distribution of the intensity of the scattered light is detected by a photodetecting array placed on the focal plane of the lens. The measured angular distribution of the scattered intensity is analyzed to determine the size distribution based on the diffraction theory for light scattering by spherical particles. The accuracy of sizing deteriorates with decreasing size. For submicron particles, the diffraction-based instruments can not be used.
Mie's light scattering theory quantitatively described the angular variation of the intensity of light scattered from a spherical particle. For a particle of diameter D much larger than the wavelength of the incident beam .lambda. (D&gt;&gt;.lambda.) most of the scattered energy is concentrated into a forward sharp cone, as can be seen in FIG. 3 (a). On the other hand, for particles of size comparable to or smaller than the wavelength of light, a large portion of the scattered energy is directed sidewards and backwards as shown in FIG. 3 (b) and 4 (c).
In the actual measurement, the scattered intensity at angles very close to zero can not be measured with accuracy because of the smearing caused by imperfection of the collecting lens, the fluctuation of wavelength of the light source and spatial nonuniformity of the refractive index of the surrounding medium or the like but also due to the restriction that the incident beam cannot be focused into a spot which is smaller than the diffraction limit of the lens. The size distribution obtained is distorted by the inaccuracy in the measured scattered intensity.
One of the present inventors has shown that the influence of the smearing on the size determination can be reduced by analyzing the profile of I(.theta.).theta., the product of the measured scattered intensity I(.theta.) and the scattering angle .theta., rather than I(.theta.). The I(.theta.).theta. at angles near zero is small and the measurement error in I(.theta.) has little influence on the determination of size distribution. For a single particle the I(.theta.).theta. profile has a peak at a specific angle determined by the ratio of the particle size to the wavelength. This peak scattering angle almost monotonously increases as the particle size decreases and is very sensitive to the change of particle size. Therefore, the particle size can be determined with accuracy from the peak scattering angle along, even for the incident beam which has a plane of polarization which changes with time. However, when the particle size becomes comparable to or smaller than the wavelength of light, the peak disappears and, as a result, the particle size cannot be determined by the above mentioned method. For a group of these fine particles, the distribution of particle size cannot be measured with accuracy.